BuckyballGraph
gives the buckyball graph.
gives the order‐n buckyball graph.
BuckyballGraph[n,"class"]
gives the order‐n buckyball graph of class "class".
Details and Options

- BuckyballGraph is also known as truncated icosahedral graph.
- BuckyballGraph[] gives the 1-skeleton of the truncated icosahedron.
- BuckyballGraph[n,"I"] gives the 1-skeleton of the (n,0)‐Goldberg polyhedron.
- BuckyballGraph[n,"II"] gives the 1-skeleton of the (n,n)‐Goldberg polyhedron.
- BuckyballGraph[n] is effectively equivalent to BuckyballGraph[n,"II"].
- BuckyballGraph takes the same options as Graph3D.



Examples
open allclose allBasic Examples (2)
Scope (4)
Options (77)
DirectedEdges (1)
By default, an undirected graph is generated:
Use DirectedEdges->True to generate a directed graph:
EdgeLabels (7)
Use any expression as a label:
Use Placed with symbolic locations to control label placement along an edge:
Use explicit coordinates to place labels:
Vary positions within the label:
Place multiple labels using Placed in a wrapper:
Any number of labels can be used:
Place multiple labels using EdgeLabels:
Use automatic labeling by values through Tooltip and StatusArea:
EdgeShapeFunction (6)
Get a list of built-in settings for EdgeShapeFunction:
Undirected edges including the basic line:
Lines with different glyphs on the edges:
Directed edges including solid arrows:
Specify an edge function for an individual edge:
Combine with a different default edge function:
Draw edges by running a program:
EdgeShapeFunction can be combined with EdgeStyle:
EdgeShapeFunction has higher priority than EdgeStyle:
EdgeStyle (4)
EdgeStyle can be combined with EdgeShapeFunction:
EdgeShapeFunction has higher priority than EdgeStyle:
EdgeWeight (3)
GraphLayout (5)
By default, the layout is chosen automatically:
Specify layouts on special curves:
Specify layouts that satisfy optimality criteria:
VertexCoordinates overrides GraphLayout coordinates:
Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:
PlotTheme (4)
VertexCoordinates (3)
By default, any vertex coordinates are computed automatically:
Extract the resulting vertex coordinates using AbsoluteOptions:
Specify a layout function along an ellipse:
Use it to generate vertex coordinates for a graph:
VertexCoordinates has higher priority than GraphLayout:
VertexLabels (13)
Use any expression as a label:
Use Placed with symbolic locations to control label placement, including outside positions:
Symbolic outside corner positions:
Symbolic inside corner positions:
Use explicit coordinates to place the center of labels:
Place all labels at the upper-right corner of the vertex and vary the coordinates within the label:
Any number of labels can be used:
Use the argument to Placed to control formatting including Tooltip:
Or StatusArea:
VertexShapeFunction (11)
Get a list of built-in collections for VertexShapeFunction:
Use built-in settings for VertexShapeFunction in the "Basic" collection:
Use built-in settings for VertexShapeFunction in the "Rounded" collection:
Use built-in settings for VertexShapeFunction in the "Concave" collection:
Combine with a default vertex function:
Draw vertices using a predefined graphic:
Draw vertices by running a program:
VertexShapeFunction can be combined with VertexStyle:
VertexShapeFunction has higher priority than VertexStyle:
VertexShapeFunction can be combined with VertexSize:
VertexShapeFunction has higher priority than VertexShape:
VertexSize (7)
By default, the size of vertices is computed automatically:
Specify the size of all vertices using symbolic vertex size:
Use a fraction of the minimum distance between vertex coordinates:
Use a fraction of the overall diagonal for all vertex coordinates:
Specify size in both the and
directions:
Specify the size for individual vertices:
VertexSize can be combined with VertexShapeFunction:
VertexStyle (4)
VertexShapeFunction can be combined with VertexStyle:
VertexShapeFunction has higher priority than VertexStyle:
VertexStyle can be combined with BaseStyle:
VertexStyle has higher priority than BaseStyle:
Applications (11)
Basic Applications (7)
Style vertices and edges of a buckyball graph:
Annotate vertices and edges of a buckyball graph:
Modify a buckyball graph parameters:
Generate a buckyball graph represented as a 2D plot:
Basic properties of the class 1 buckyball graph; the number of vertices:
Basic properties of the class 2 buckyball graph; the number of vertices:
Graph Theory (4)
Properties & Relations (2)
The ratio of the number of vertices to the number of edges is :
BuckyballGraph[1] is the graph corresponding to the truncated icosahedron:
Text
Wolfram Research (2022), BuckyballGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BuckyballGraph.html.
CMS
Wolfram Language. 2022. "BuckyballGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BuckyballGraph.html.
APA
Wolfram Language. (2022). BuckyballGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BuckyballGraph.html